Finite element analysis of the effect of shape memory
alloy on the stress distribution and contact pressure in total knee
replacement.

Abstract:

As a step towards developing a biomaterial for femoral component of
total knee replacement, the goals of this study were to introduce NiTi
shape memory alloy as a promising material for orthopedic implant and to
evaluate the effect of different material properties on contact behavior
of the joint and stress distribution of the femoral bone using finite
element method. Two separate finite element analyses were performed; one
with rigid bones and the other with deformable femur, at 0 degree of
flexion angle under static loading condition. The results showed no
difference between the various materials with regards to the peak
contact pressure but considerable difference with regards to the Von
Mises stresses. The results also demonstrated that stress values closer
to the natural femur were obtained for NiTi implant compared with other
metals. Hence, this finite element analysis showed that NiTi shape
memory alloy can reduce the stress shielding effect on the femoral bone.

Increasing trend to replace degraded and lost biological materials
by artificial organs make total joint replacements as one of the most
important current discussions in orthopedic, especially for hip and
knee. One statistical study predicted that by the end of 2030, the
number of total hip replacements will increase by 174% and total knee
arthoplasties is estimated to grow by 673% from the present rate (1). It
has been found that, current materials including stainless steel,
titanium alloys and cobalt chromium with small amount of molybdenum
(Co-Cr-Mo), which are used to fabricate femoral component of total knee
replacement (TKR), cause to failure of implant after long-term use in
the human body due to not fulfilling some vital requirements (2,3).
Deficiencies of the presently used materials and yet-increasing trend to
replace knee joint make it crucial to accelerate efforts on
biomaterials. Shape memory alloys (SMA), made of NiTi, provide new
insights in the design of biomaterials for artificial organs and
advanced surgical instruments due to their superior properties (4-6).
This material has been introduced as a good choice for orthopedic
application due to combination of high recovery strain, high strength,
unique high fatigue resistance, ductile properties, high dampening
capacity (2,3,7) and enhanced biocompatibility (8-15). It has been
reported that NiTi has high wear resistance compared to the Co-Cr-Mo
alloy. In addition, it has a relatively low Young's modulus of
d"48 GPa at body temperature that is much lower than that of
current materials. These two last properties appear to be more important
for femoral component of TKR to reduce wear of ultra high molecular
weight polyethylene (UHMWPE), and to prevent femoral bone loss. NiTi
(SMA), therefore can satisfy the biomaterial requirements which are
generally favorable for orthopedic implants. However the biomaterial
aspects of joint replacement is of importance, long-term performance of
an implant only be attained by considering the biomechanical aspects of
joint replacement simultaneously. Peak contact pressure and stress
shielding effect are two biomechanical parameters that have critical
importance in success of TKR. Peak contact pressure contributes in wear
of UHMWPE in TKR which has been known as a main reason for failure of
knee joint arthroplasty so far (16,17). Femoral bone loss as a common
feature after total knee arthroplasties is partially attributed to
stress shielding of the bone by the prosthesis (18). These biomechanical
aspects have been predicted either by finite element analyses (FEA) or
through in vitro experiments. However there have been many FEA and
experimental studies on contact characteristics of TKR (19-24) and
stress shielding of the bone (25-32), all of them investigated the
existing biomaterials rather than promising ones. In this study FEA is
used as a tool for material selection (33) since it enables the
possibility of changing material properties of components and predicting
the behavior before manufacturing any prototypes. So the objective of
this paper is to examine NiTi shape memory alloy as a femoral component
of TKR by measuring peak contact pressure of the tibiofemoral joint and
stress distribution of the femoral bone through FEA. In this regard
after modeling the human knee and validation, material properties of the
natural knee are replaced with those of Co-Cr alloy, Ti alloy and NiTi
SMA.

Materials and Methods

Geometries of bony structures and soft tissues were taken from a
healthy human knee of a 24-year old man. Solid models of the femur and
tibia and geometries of soft tissues including articular cartilages and
menisci, were obtained from the magnetic resonance images (MRI).

[FIGURE 1 OMITTED]

Each image was taken at 3.2 mm interval in a sagittal plane. These
data were used to create a three dimensional computer aided design (3D
CAD) model in order to import into ABAQUS 6.8 software for FEA. The
model consisted of two bony structures (femur and tibia), articular
cartilages and menisci. The model does not include ligaments. Figure 1
shows different parts of the knee joint model. The finite element mesh
generation was performed resulting in 41709 linear 4-noded tetrahedron
elements for articular cartilages and menisci (25293 for femoral
cartilage, 9130 for tibial cartilage, 3866 for lateral meniscus and 3420
for medial meniscus). Two separate simulations were performed where in
one simulation bony structures were modeled as rigid with 16414 linear
3-noded rigid triangular elements and in the second one, deformable
femur was meshed by linear 4-noded tetrahedron elements.

Contact pairs were defined as femoral cartilage/medial meniscus,
femoral cartilage/lateral meniscus, tibial cartilage/medial meniscus,
tibial cartilage/lateral meniscus and tibial cartilage /femoral
cartilage resulting in six contact-surface pairs. General contact
condition involving small sliding of pairs was applied on the model and
all contact surfaces were assumed to be frictionless.

In order to validate the model, static loads equivalent to 0, 500,
734, 800, 1000, 1500, 2000 and 2500 N were applied on the model at 0[??]
flexion angle and the results were compared with previous experimental
and FEA studies(34-37). The cartilage was defined as a homogeneous
linearly isotropic elastic material with E=15MPa and [??]=0.475 (38) and
the menisci were modeled as linearly elastic, transversely isotropic
material with moduli of 20MPa in the radial and axial directions and
140MPa in circumferential direction. The in-plane and out-of-plane
Poisson's ratio were 0.2 and 0.3 respectively and the shear modulus
was considered 50MPa (39-42). Horn attachments were represented by 10
linear springs with 200 N/mm stiffness resulted in 2000N/mm total
stiffness.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The femur and tibia were modeled as rigid in first simulation
because they have much larger stiffness compared to that of soft
tissues. This is time efficient in a non-linear analysis and as
confirmed from previous study [37] that this simplification has no
considerable effect on contact variables. In the second simulation, the
femur was modeled as deformable material under static load of 800 N at
[0.sup.^] flexion angle to determine stress distribution on the
cancellous bone. Femoral cortical bone was modeled as orthotropic
elastic with [E.sub.1]=12 (GPa), [E.sub.2]=13.4 (GPa), [E.sub.3]=20
(GPa), [G.sub.12]=4.53 (GPa), [G.sub.13]=5.61 (GPa), [G.sub.23]=6.23
(GPa), [[??].sub.12]=0.38, [[??].sub.13]=0.22 and [[??].sub.23]=0.24
(43) where direction 1,2 and 3 were radial, circumferential and the long
axis of the bone respectively. The cancellous bone was assumed to behave
homogeneous linearly isotropic with modulus of 0.4 GPa and a
Poisson's ratio of 0.3 [37]. For boundary conditions, in both
simulations, the tibia was constrained from rotation and translation in
all directions and femur was fixed from rotating in all three directions
and was free to translate in anterior-posterior, medial-lateral and
inferior-superior axes. Figure 2 shows the mesh generation of the knee
joint.

[FIGURE 4 OMITTED]

For evaluation of the metallic biomaterial performance, it was
assumed that the geometry of the implant is the same as that of natural
knee. The material properties of femoral cartilage were replaced by
cobalt chromium alloy, Ti alloy and NiTi shape memory alloy. Cobalt
chromium alloy, Ti-6Al-4V and NiTi (SMA) were defined as homogeneous
linearly isotropic elastic materials with E=200GPa, [??]=0.3, E=114 GPa,
[??]=0.32 (44) and E=39, [??]=0.46 (45,46) respectively. The material
properties of UHMWPE were used to replace the menisci. Stress strain
behaviors of UHMWPE and the SMA material are shown in Figure 3 (a) and
(b). Since the strain value is small, for the material study, linear
elastic homogeneous behavior was assumed.

Results and Discussion

Verifying the results of FEA for natural knee

The results of peak contact pressure for different magnitudes of
force for natural (human) knee are demonstrated in Figure 4. The
stresses were calculated at the contact regions and it was found that
the total stress multiples by area equilibrate the total applied load in
the knee joint which is transferred through the femur-meniscus,
femur-tibia, and meniscus-tibia. The computed reaction forces also are
in the equilibrium with the applied load at each loading condition.
However the FE solution may have satisfied the equilibrium, representing
that the finite element solution was accurate to some extent, confidence
in the verification of the model itself were achieved by comparing the
predicted values of the peak contact pressure with the previously
reported simulated and experimental data. Among the various researches
that have measured the peak contact pressure on the tibiofemoral joint
(34-37,48-51), the following researches were used for comparison to the
data of the present study (34-37).

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

Table 1 shows the comparisons between the obtained values of peak
contact pressure from the present work with those of previous studies.
For calculation of the differences with the experimental values, the
average was considered. It can be seen that, the present results
compares quite well with other researches with maximum difference of
about 3.38% and average difference of 1.728%. Hence the obtained data
from present study is therefore verified. Furthermore the results of
deformable model were presented in Table 2 in order to validate those
results.

Contact pressure for various materials

Maximum contact stresses were measured on the polyethylene parts
and also on the tibial cartilage when femoral part was chromium cobalt
alloy, Ti-6Al-4V and NiTi shape memory alloy. The results were shown in
table 3. It can be seen that there were no major difference in the
results for different materials.

For more confidence on the results, the menisci were replaced by a
flat plate of UHMWPE and the maximum contact pressure was obtained on
the plate, but it was found that the magnitude of this parameter was
same for all the materials.

Stress distribution for different materials

In this section all stresses were normalized to those determined
from the model of an intact femur. The stress distributions were
analyzed for all models under transverse and sagittal planes along 4
paths placed parallel to medial-lateral direction and the long axis of
the bone respectively as shown in Figure 5 and Figure 6. However all the
implant materials give lower magnitude of stresses on the femur (with
the same trend), from the comparison of different materials, it can be
seen that the stress distribution on the femur with NiTi (SMA) are much
closer to that of intact femur, for example table 4 shows the
differences in normalized Von Mises stresses with natural femur in path1
(Figure 5a) at proximal distance of 0, 2, 7, 12, 17 mm for various
materials. The general order of stress values similarity to the natural
femur in all paths is as follow:

Intact Femur> NiTi>Ti-6Al-4V>Cr-Co alloy

Figure 7 also shows the similarity of stress patterns of the
implant materials with natural knee. It can be observed that NiTi has
the most similar pattern with the human knee.

Conclusion

NiTi shape memory alloys (SMA) have been introduced to have great
potential for medical application such as orthopedic implantation. The
results of the present study under static load of 800 N at 0^ flexion
angle showed no difference on peak contact pressure for different
materials. Also it has been found that NiTi (SMA) reduced Von Mises
stresses less than Cr-Co alloy and Ti-6Al-4V. So it can be concluded
that NiTi SMA can reduce the stress shielding effect and consequently
loss of the femoral bone which provides loosening of the implant.

However the limitation of this study is the assumption of same
geometry of the implant and human knee. Also the results were limited to
the static loading condition. So future research works will examine the
effect of NiTi shape memory alloy on the actual implant geometries and
under dynamic loading situation.

References

(1.) Kurtz S, Ong K et al., Projections of primary and revision hip
and knee arthroplasty in the United States from 2005 to 2030. Journal of
Bone and Joint Surgery--Series A, 2007. 89(4): p. 780-5.